The digital display of three dimensional objects in a conventional two dimensional screen or printable substrate is possible in several ways. The most instructive display is usually made possible by an isometric-perspective representation. However, such a presentation, when required to be computed by a suitable software involves complicated computations that consume precious computing time, memory, hardware, complicated software and other scarce computer resources. In addition, in a perspective view the "rear" parts or surfaces of the object are always hidden behind the frontal parts. Moreover, for many purposes, the display may be reduced to a simplified top, bottom or side view, inwhich two Cartesian dimensions are represented by the X-Y raster display of the screen or the substrate, and "depths" and "heights" of the third Z dimension or coordinate are represented by altitude lines or coloring. Such a display is relatively economical in the consumption of scarce computer resources and since only one "surface" is shown, it seldom leaves hidden parts or surfaces when presented from an appropriate angle.
The conventional way by which a surface view is computed, is by computing the values of the third dimension of each pixel, and drawing equivalence lines, whereby each equivalence line represents equivalent "height" or "depth". For enhancing the view, it is common to provide coloring or shadowing characteristics to the lines or the areas between them. Shadowing or coloring which are relative to the abruptness of steep slopes or density of equivalence lines is another possible representation, once such equivalence lines are computed and defined. Nevertheless, the computing of such equivalence line still requires substantial computing resources as well as the determination of the coloring or the shadowing.
It is therefore an object of the invention present to provide a novel method and device for displaying a third dimension of an object or a surface.
It is another object of the present invention to provide a method and device for use in conjunction of conventional computer monitor, TV screen, digital print on a printable substrate, or other two or three dimensional display means.
It is a further object of the invention, to provide a method and a device for displaying a fourth or a fifth dimension of an object, in a two or three dimensional display means, correspondingly.
Yet, a further object of the present invention is to provide a method and a device for defining by a single step the coloring or shading of each pixel for a given function representing an "object", without computing equivalence lines of the object.
It is yet another object of the present invention to provide a method and a device for displaying on an N-dimensional displaying means, a further "N+1" dimension or further "N+2" dimensions.
Still, another object of the invention is to provide a method and a device that will involve, minimal computing steps, and will use minimal computer resources.
It is still a further object of the invention to provide a method and a device that will adapt for use with the conventional hardware or software bywhich each numerical value has a pre-defined coloring or shading.
These and other objectives are provided by the invention described below.